Question

If ABCD is a rectangle, AD = 9, AC = 22, B Ж X D Find the Length of all the Segments in the Parallelogram. AD AC = CD =

Answer 1

Since we're working on a rectangle, we know that the diagonals intercect right in the middle, and that they're all equal.

This way,

`AC=BD=22`

And

`AE=BE=DE=CE=(1)/(2)AC=11`

Now, we also know that

`AD=BC=9`

And using the Pythagorean theorem, we have that:

`AD^2+CD^2=AC^2`

Solving for CD,

`\begin{gathered} CD=\sqrt[]{AC^2-AD^2} \\ \rightarrow CD=20.07 \end{gathered}`

And we know that:

`AB=DC=20.07`

This way, the final answers would be:

`\begin{gathered} AD=9 \\ AC=22 \\ CD=20.07 \\ AB=20.07 \\ BD=22 \\ BC=9 \\ AE=11 \\ BE=11 \\ CE=11 \\ DE=11 \end{gathered}`